A theoretical study on the ionization dynamics of carbon atom irradiated with a few-cycle, intense laser field is performed within a quasiclassical model to get mechanistic insights into an earlier reported carrier-envelope phase dependency of ionization probabilities of an atom [Phys. Rev. Lett. 2013, 110, 083602]. The carrier-envelope phase of the laser pulse is found to govern the overall dynamics, reflecting its importance in controlling electronic motion. To understand the origin of this effect, individual trajectories were analyzed at a particular laser intensity. We found that a variation in the carrier-envelope phase affects the angle of ejection of the electrons and subsequently the attainment of the desired final state.